Recording medium for recording data include magnetic discs, optical discs, magneto-optical discs, and magnetic tapes, for example. When data is digitally recorded on, or read back from, a recording medium, it is preferable that the data is recorded at a high density. Partial response systems are usually used for this purpose. High-density recording is then possible by adopting a PRML (Partial Response with Maximum Likelihood) method that combines the partial response equalization and Viterbi detection.
During readback it is desirable that the signal does not have a dc (direct current) component, or at least that the dc component is as small as possible. This means that the power spectral density function of the recorded sequence at dc equals zero. Such sequences are said to be dc-free. It is desirable that the sequence be as dc-free as possible because it is necessary to ensure that, for example, errors due to variations in a reference level during quantization of the read back signal do not occur. It is also desirable that the sequence be substantially dc-free to ensure that fluctuations do not occur in error signals, such as tracking error signals, occurring in the servo control.
With the recorded symbols taken to be +1 and −1, so that +1 corresponds to binary 1 and −1 corresponds to binary 0, the so-called running digital sum (RDS) is a standard measure for evaluating the dc component. The RDS is the total sum of the recorded symbols from the time of starting the sequence. A small RDS absolute value, namely low disparity between +1s and −1s, means that the content of the dc component is low. Sequences with equal numbers of +1s and −1s are referred to as being “balanced.” Balanced sequences do not have a dc component. Further measures of suppression of low frequencies of a signal are so called “RDS of higher order.” The higher order RDS can be computed recursively in such a way that the RDS of the order i is an algebraic sum of values of an RDS of lower order, i−1.
Partial response systems, or system with a controlled inter-symbol interference, are commonly described by so-called “target partial response polynomials” having the form h(D)=h0+h1D+h2D2+ . . . +h1D1, where D is a time delay operator. The values of the polynomial coefficients h1, h2, . . . , h1 represent values of a sampled channel response to an isolated impulse. The typical form of a partial response polynomial used in magnetic disc devices exploiting longitudinal recording is h(D)=(1−D)m(1+D)n where m and n are positive integers. In optical recording systems and in perpendicular magnetic recording systems the typical form of a partial response polynomial is h(D)=(1+D)m. If the partial response polynomial contains a term (1−D), then the frequency response of such a channel does not pass a dc component, and RDS control to make the maximum absolute value of the RDS of the modulation code sequence small is therefore not needed. However, for partial response polynomials that do not have factor (1−D), the frequency response of a channel does have a dc component and RDS control does have to be carried out.
Modulation coding can be used to obtain dc-free sequences. Modulation coding may be implemented, for example, by parsing digital information that is to be recorded into strings of bits, called message words. Each message word is then used to select a codeword from a codebook. The codewords in the codebook are of length n bits, where the codeword bits define a recorded sequence. In other words, the codeword bits define a sequence of symbols to be recorded on a medium. However, efficient or high-rate dc-free modulation codes that can ensure bounded value of RDS, without adding an excessive number of redundant bits to the information to be recorded, typically require both codewords and codebooks of larger sizes as discussed further below.
The measure of code efficiency is a parameter called “code rate,” which represents the ratio between m, the message word length and n, the codeword length. Furthermore, in recording systems, it is desirable that a modulation code have a rate higher than 8/9, so that more information can be written on the recording medium. Codes having a relatively long codeword length are required for rates above 8/9. Also, large codebooks are required where the codewords in the codebooks are dc-free. For example, a code of rate 16/17 requires a codeword length of 17 and a codebook size of 65536. Such large codebooks, however, typically require the implementation of complex circuitry and require relatively high power consumption and a large area on integrated circuits. Also, the larger the codebook, the more time it takes to access codewords in the codebook. With current technology, it would be extremely costly, if even possible, to design a codebook with 65536 words of length 17. Thus, there is a need for a method and apparatus for generating high rate codes that are dc-free and lend themselves to a low complexity implementation.
Typically, an error correcting code is used in conjunction with a modulation code. Error correcting codes introduce additional bits to a signal to form an encoded signal. The additional bits improve the ability of a system to recover the signal when the encoded signal has been corrupted by noise introduced by a recording channel.
Examples of a modulation codes are the 8-10 code adopted in digital audio tape recorders (DAT), the EFM (Eighteen to Fourteen Modulation) code adopted in compact disc (CD) players, and the EFMPlus code adopted in digital versatile disc (DVD) players. Various codes for eliminating dc free components are known. Examples of error correcting codes include Reed-Solomon codes adopted in magnetic and optical recording systems.
Typically, data is first encoded using an error correcting code, and then using a modulation code. This is called a traditional error-correcting-modulation coding concatenation scheme. When a traditional error correcting-modulation coding concatenation scheme is used together with high rate dc-free codes, the error multiplication is inevitable. Error multiplication means that error in one recorded bit produces errors on several bits in the decoded data. This effect is a consequence of the nonlinear structure of a modulation decoder. Another scheme, so called inverse concatenation, puts modulation encoding before error control coding, and modulation decoding after modulation decoding. In this way, the errors are first corrected by an error correcting code, and the error multiplication is prevented. However, the error correcting encoder does not necessarily produce balanced codewords nor low disparity codewords, hence undoing the disparity control introduced by the modulation encoder. Therefore, there is a need for a method and apparatus for generating high rate codes that are at the same time dc-free and possess error control capabilities.